It has been shown that non-Markovian retarded effects arising from the large separation distances between, for instance, a single atom and the waveguide end [1]}, [2]}, [3]}, different coupling ports of a giant atom [4]}, and far apart atoms [5]}, [6]}, [7]} can markedly modify the dynamics. When the traveling time of photons or phonons in the waveguide between different atom-waveguide coupling channels is large enough compared with the inverse of the atomic relaxation rate, the dynamics can exhibit prominent non-Markovianity and thus can not be predicted by common Markovian treatments. This suggests that non-Markovian retarded effect should be taken into account when considering nonlocal couplings that are inevitable in many large-scale systems (e.g., quantum networks). In particular, a counterintuitive phenomenon referred to as “superradiant paradox” arises if the separation \(L\)  between atoms satisfies \(l_{c}/2<d<l_{c}\) , where \(l_{c}\)  is the coherent length of photons emitted from the emitters to the waveguide [5]}, [6]}. As the number of atom increases, the non-Markovianity is shown to be non-negligible even for small separations  [10]}. Such non-Markovian dynamics in single-photon waveguide QED can be solved semi-analytically via a real-space approach [11]} and fully analytically via a diagrammatic method [12]}.
